A school had enrolment of 1400 pupils.when 100 boys and 3/8 of the girls were absent,the number of girls present was equal to the number of boys present.how many more girls then boys were in the school
Answers
Answer:
There are 200 more girls than boys in the school.
Step-by-step explanation:
Let total number of boys in the school = a
Let total number of girls in the school = b
=> a + b = 1400 ......(Eqn 1)
No. of boys absent = 100
No. of girls absent = (3/8)*b
Now,
No. of boys/girls present = Total no. of boys/girls - No. of boys/girls absent
Hence:
No. of boys present = a - 100
No. of girls present = b - (3/8)*b
= (5/8)*b
We are given that:
No. of girls present = No. of boys present
Therefore,
(5/8)*b = (a-100)
5b/8 = a - 100
5b = 8(a - 100) ........Eqn 2
From Eqn 1, we get:
b = 1400 - a
Substituting this in Eqn 2, we get:
5(1400 - a) = 8(a - 100)
7000 - 5a = 8a - 800
13a = 7800
a = 600
Now,
b = 1400 - a
= 1400 - 600
= 800
No. of boys = 600
No. of girls = 800
No. of girls - No. of boys = 800 - 600 = 200
Final answer: There are 200 more girls than boys in the school.